Computerized image processing applications that require 3-D modeling of large scenes, or image compositing of a large scene typically use images acquired by cameras with wide fields of view. Images taken with cameras having wide fields of view suffer from non-linear distortions due to simplified lens construction and lens imperfections. In such images, distortion effects can be removed by calibrating the camera and subsequently undistorting the input image. Distortion can also be present in images taken through other types of lenses.
In general, there are two forms of distortion, namely radial distortion and tangential distortion. In many cases, the recovery of camera parameters is disconnected from the process which detects distorted features in an image. Although this does not present a problem when feature detection is correct, directly linking the feature detection to parameter estimation can result in a more robust recovery, especially in the presence of noise.
There has been significant work done on camera calibration, but many known methods require taking images of specific calibration patterns with exactly known dimensions. There is a class of work done on calibrating the camera using the scene image or images themselves, and possibly taking advantage of special structures such as straight lines, parallel straight lines, perpendicular lines, and so forth.
In one prior art method, a minimum vanishing point dispersion constraint is used to estimate both radial and tangential (decentering) lens distortion. However, there the user has to manually group parallel "calibration" lines together.
In another known method, a number of parallel plumb lines are used to compute the radial distortion parameters using an iterative gradient-descent technique involving a first order Taylor's expansion of a line fit function. Points on the parallel plumb lines are manually extracted. Such a process can be time consuming; for example, measuring 162 points from horizontal lines and 162 points from vertical lines may take several hours.
Another method uses point correspondences between multiple views to extract radial distortion coefficients. There, epipolar and tri-linear constraints are used, and a search is performed for the amount of radial distortion that minimizes the errors in these constraints.
Photogrammetry methods usually rely on using known calibration points or structures, for example, using plumb lines to recover distortion parameters, or corners of regularly spaced boxes of known dimensions for full camera calibration. A more flexible known arrangement requires that all points used for the calibration are coplanar, and that there are identified horizontal and vertical points among the calibration points. Projective invariants can also be used to recover radial distortion coefficients.
In other image processing applications unrelated to distortion correction, such as the tracking of human facial features, and the reconstruction of objects using cells, active deformable contours, or "snakes" have been used to outline features in images. The various forms of snakes include the notion of "inflating contour" to reduce sensitivity to initialization at the expense of an increased number parameters, or using an "active contour." In these methods, the snakes, some of which may be parameterized, are generally independent of each other. It would be advantageous to recover distortion parameters (.kappa.) from a single image without prior knowledge of the camera parameters. It would also be a further advantage when the recovery can be done directly from any image.